Geodesic
The configuration space of a robotic arm in a tunnel of width 2
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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We study the motion of a robotic arm inside a rectangular tunnel of width 2. We prove that the configuration space S of all possible positions of the robot is a CAT(0) cubical complex. Before this work, very few families of robots were known to have CAT(0) configuration spaces. This property allows us to move the arm optimally from one position to another. 
@article{DMTCS_2020_special_379_a84,
     author = {Ardila, Federico and Bastidas, Hanner and Ceballos, Cesar and Guo, John},
     title = {The configuration space of a robotic arm in a tunnel of width 2},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6402},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6402/}
}
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Ardila, Federico; Bastidas, Hanner; Ceballos, Cesar; Guo, John. The configuration space of a robotic arm in a tunnel of width 2. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6402. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6402/

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